Abstract
We consider a N – S box system consisting of a rectangular conductor coupled to a superconductor. The Green functions are constructed by solving the Bogoliubov-de Gennes equations at each side of the interface, with the pairing potential described by a step-like function. Taking into account the mismatch in the Fermi wave number and the effective masses of the normal metal – superconductor and the tunnel barrier at the interface, we use the quantum section method in order to find the exact energy Green function yielding accurate computed eigenvalues and the density of states. Furthermore, this procedure allow us to analyze in detail the nontrivial semiclassical limit and examine the range of applicability of the Bohr-Sommerfeld quantization method.
Highlights
There is an increasing technological interest in the study of normal-conductor(N ) ballistic quantum dots attached to a superconductor(S), giving rise to the coherent scattering of electron into holes and at the superconductor-conductor interface. This peculiar phenomena known as Andreev reflection is an important concept, necessary to understand the properties of nanostructures with N − S hybrid structures, commonly called Andreev billiards[1]
The N −S box system consists of a rectangular conductor N of height w and width a attached to a superconductor S
We find that every phase contribution is affected by a term Θim taking into account the fact that the waves functions can go further into the superconductor region. This is a correction applied to the usual tunneling term θ, since it depends on it and the superconductor material physical parameters
Summary
There is an increasing technological interest in the study of normal-conductor(N ) ballistic quantum dots attached to a superconductor(S), giving rise to the coherent scattering of electron into holes and at the superconductor-conductor interface. This peculiar phenomena known as Andreev reflection is an important concept, necessary to understand the properties of nanostructures with N − S hybrid structures, commonly called Andreev billiards[1]. With x′ = x′′ = 0 on the section, we obtain the energy Green function Gm(E) imposing that at the eigenenergy:. We will see that this strategy is useful when searching for a semiclassical description
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